Chapter 21: Q. 58 (page 597)

A heat engine using a monatomic gas follows the cycle shown in FIGURE P $21.58$ .
a. Find $W_{s}, Q$ , and ${ΔE}_{th}$ for each process in the cycle. Display your results in a table.
b. What is the thermal efficiency of this heat engine?

Short Answer

Expert verified

a. Table for process of cycle is .

b. The thermal efficiency is $15 %$ .

Step by step solution

Calculation for work done in first process (part a)

(a) .

The third process is adiabatic,

So the maximal pressure is,

$p_{1} V_{1}^{γ} = p_{3} V_{3}^{γ}$

$\Rightarrow p_{1} = {(\frac{V_{3}}{V_{1}})}^{γ} p_{3}$

So,

$p_{1} = 6^{1.67} \times 100 atm$

$= 1993 kPa$

The first process is isobaric,

so,

$T_{1} = \frac{V_{2}}{V_{1}} T_{2}$

$= 100 K$

The heat is,

$Q = \frac{p_{2} V_{2}}{{RT}_{2}} C_{p} (600 - 100) m^{3}$

$\approx 8300 J$

The work done is,

role="math" localid="1650269695241" $W = 1993 \times 10^{3} J \times 500 \times 10^{- 6}$

$\approx 1000 J$

Calculation for work in second process (part a) solution

For second process the work done is null,

$Q = \frac{p_{2} V_{2}}{{RT}_{2}} C_{p} ΔT$

$= \frac{p_{2} V_{2}}{{RT}_{2}} C_{p} \frac{p_{2} - p_{3}}{p_{2}} T_{2}$

$= \frac{C_{p} V_{2} (p_{2} - p_{3})}{R}$

So,

$Q = \frac{12.5 \times 6 \times 10^{- 4} m^{3} \times 1893 \times 10^{3} J}{8.314 Ω}$

$\approx 2850 J$

The third point is,

$T_{3} = \frac{p_{3}}{p_{2}} T_{2}$

role="math" localid="1650270106364" $= \frac{100 atm}{1993 kPa} \times 600 m^{3}$

$= 30.1 K$

The heat is,

$Q = \frac{p_{2} V_{2}}{{RT}_{2}} C_{v} (T_{3} - T_{2})$

$= - 210 J$

Result for process in cycle part(a) solution

Calculation for thermal efficiency (part b)

From the table,

The total heat input is $5240 J$ ,

The work done is $790 J$ .

The efficiency is,

$η = \frac{790 J}{5240 J}$

$= 15 %$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A heat engine using a monatomic gas follows the cycle shown in FIGURE P $21.58$ .
a. Find $W_{s}, Q$ , and ${ΔE}_{th}$ for each process in the cycle. Display your results in a table.
b. What is the thermal efficiency of this heat engine?

Short Answer

Step by step solution

Calculation for work done in first process (part a)

Calculation for work in second process (part a) solution

Result for process in cycle part(a) solution

Calculation for thermal efficiency (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Force

Kinematics Physics

Geometrical and Physical Optics

Linear Momentum

Thermodynamics

Study anywhere. Anytime. Across all devices.

A heat engine using a monatomic gas follows the cycle shown in FIGURE P21.58.a. Find Ws,Q, and ΔEthfor each process in the cycle. Display your results in a table.b. What is the thermal efficiency of this heat engine?

Short Answer

Step by step solution

Calculation for work done in first process (part a)

Calculation for work in second process (part a) solution

Result for process in cycle part(a) solution

Calculation for thermal efficiency (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Force

Kinematics Physics

Geometrical and Physical Optics

Linear Momentum

Thermodynamics

Study anywhere. Anytime. Across all devices.

A heat engine using a monatomic gas follows the cycle shown in FIGURE P $21.58$ .
a. Find $W_{s}, Q$ , and ${ΔE}_{th}$ for each process in the cycle. Display your results in a table.
b. What is the thermal efficiency of this heat engine?